Suppose I author a book as a PDF with half-letter pages. I want to print 4 of these page on each letter sheet (2 tiled on the front, 2 on the back), stack them on top of each other, and bind through the middle.
It seems to me that for instance if my book had 16 pages, sheet 1 would have to contain pages 1 and 16 on the front side, page 2 behind 1 and 15 behind 16. Then sheet 2 would need to be printed with pages 3 and 14 on one side, 4 behind 3 and 13 behind 14. Yet it seems that most printers and PDF converters produce output so that sheet 1 will contain pages 1 and 2, with 3 and 4 behind them, then sheet 2 will contain pages 5, 6 on one side and 7, 8 on the other.
What is the style of printing that I want called? Is it common for consumer printers to support it? How do book printers deal with this problem? Do they just generate a PDF that already has the pages laid out in the right order (tiled and arranged on full-size paper), and then simply print that? How?